Skip to main content
Mathematics LibreTexts

2.10: Proficiency Exam

  • Page ID
    57161
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Proficiency Exam

    For the following problems, simplify each of the expressions.

    Exercise \(\PageIndex{1}\)

    \(8(6−3)−5\cdot4+3(8)(2)\div4\cdot3\)

    Answer

    \(40\)

    Exercise \(\PageIndex{2}\)

    \(\{2(1+7)^2\}^0\)

    Answer

    \(1\)

    Exercise \(\PageIndex{3}\)

    \(\dfrac{1^8 + 4^0 + 3^3(1 + 4)}{2^2(2 + 15)}\)

    Answer

    \(\dfrac{137}{68}\)

    Exercise \(\PageIndex{4}\)

    \(\dfrac{2 \cdot 3^4 - 10^2}{4 - 3} + \dfrac{5(2^2 + 3^2)}{11 - 6}\)

    Answer

    \(75\)

    Exercise \(\PageIndex{5}\)

    Write the appropriate relation symbol (>, <) in place of the *.

    \(5(2+11)∗2(8−3)−2\)

    Answer

    >

    For the following problems, use algebraic notation.

    Exercise \(\PageIndex{6}\)

    \((x-1)\) times \((3x \text{plus} 2)\)

    Answer

    \((x-1)(3x+2)\)

    Exercise \(\PageIndex{7}\)

    A number divided by twelve is less than or equal to the same number plus four.

    Answer

    \(\dfrac{x}{12} \le (x+4)\)

    Exercise \(\PageIndex{8}\)

    Locate the approximate position of \(−1.6\) on the number line.

    Screen Shot 2021-02-08 at 8.16.07 PM.png

    Answer

    Screen Shot 2021-02-08 at 8.16.27 PM.png

    Exercise \(\PageIndex{9}\)

    Is \(0\) a positive number, a negative number, neither, or both?

    Answer

    Zero is neither positive nor negative.

    Exercise \(\PageIndex{10}\)

    Draw a portion of the number line and place points at all even integers strictly between 14 and 20.

    Answer

    Screen Shot 2021-02-08 at 7.54.59 PM.png

    Exercise \(\PageIndex{11}\)

    Draw a portion of the number line and place points at all real numbers strictly greater than −1 but less than or equal to 4.

    Answer

    Screen Shot 2021-02-08 at 7.55.41 PM.png

    Exercise \(\PageIndex{12}\)

    What whole numbers can replace x so that the following statement is true? \(-4 \le x \le 5\).

    Answer

    \(0,1,2,3,4,5\)

    Exercise \(\PageIndex{13}\)

    Is there a largest real number between and including 6 and 10? If so, what is it?

    Answer

    Yes, 10.

    Exercise \(\PageIndex{14}\)

    Use the commutative property of multiplication to write \(m(a+3)\) in an equivalent form.

    Answer

    \((a + 3)m\)

    Exercise \(\PageIndex{15}\)

    Use the commutative properties to simplify \(3a4b8cd\).

    Answer

    \(96abcd\)

    Exercise \(\PageIndex{16}\)

    Use the commutative properties to simplify \(4(x−9)2y(x−9)3y\).

    Answer

    \(24y^2(x-9)^2\)

    Exercise \(\PageIndex{17}\)

    Simplify \(4\) squared times \(x\) cubed times \(y\) to the fifth.

    Answer

    \(16x^3y^5\)

    Exercise \(\PageIndex{18}\)

    Simplify \((3)(3)(3)aabbbbabba(3)a\).

    Answer

    \(81a^5b^6\)

    For the following problems, use the rules of exponents to simplify each of the expressions.

    Exercise \(\PageIndex{19}\)

    \((3ab^2)^2(2a^3)^3\)

    Answer

    \(71a^{11}b^7\)

    Exercise \(\PageIndex{20}\)

    \(\dfrac{x^{10}y^{12}}{x^2y^5}\)

    Answer

    \(x^8y^7\)

    Exercise \(\PageIndex{21}\)

    \(\dfrac{52x^7y^{10}(y-x^4)^{12}(y+x)^5}{4y^6(y-x^4)^{10}(y+x)}\)

    Answer

    \(13x^7y^4(y-x^4)^2(y+x)^4\)

    Exercise \(\PageIndex{22}\)

    \((x^ny^{3m}z^{2p})^4\)

    Answer

    \(x^{4bn}y^{12m}z^{8p}\)

    Exercise \(\PageIndex{23}\)

    \(\dfrac{(5x+4)^0}{(3x^2-1)^0}\)

    Answer

    \(1\)

    Exercise \(\PageIndex{24}\)

    \(\dfrac{x^∇x^□y^Δ}{x^Δy^∇}\)

    Answer

    \(x^{∇+□-Δ}y^{Δ-∇}\)

    Exercise \(\PageIndex{25}\)

    What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?

    Answer

    A variable


    This page titled 2.10: Proficiency Exam is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

    • Was this article helpful?